SIE[mu] can be used as input for D-1-dimensional \sigma^{\mu } with D-4-dimensional Lorentz index \mu and is transformed into PauliSigma[LorentzIndex[mu,D-4],D-4] by FeynCalcInternal.
Overview, PauliSigma, SI.
SIE[\[Mu]]\hat{\sigma }^{\mu }
SIE[\[Mu], \[Nu]] - SIE[\[Nu], \[Mu]]\hat{\sigma }^{\mu }.\hat{\sigma }^{\nu }-\hat{\sigma }^{\nu }.\hat{\sigma }^{\mu }
StandardForm[FCI[SIE[\[Mu]]]]
(*PauliSigma[LorentzIndex[\[Mu], -4 + D], -4 + D]*)SIE[\[Mu], \[Nu], \[Rho], \[Sigma]]\hat{\sigma }^{\mu }.\hat{\sigma }^{\nu }.\hat{\sigma }^{\rho }.\hat{\sigma }^{\sigma }
SIE[\[Mu], \[Nu], \[Rho], \[Sigma]] // StandardForm
(*SIE[\[Mu]] . SIE[\[Nu]] . SIE[\[Rho]] . SIE[\[Sigma]]*)SIE[\[Alpha]] . (SISE[p] + m) . SIE[\[Beta]]\hat{\sigma }^{\alpha }.\left(m+\hat{\sigma }\cdot \hat{p}\right).\hat{\sigma }^{\beta }